FLT CREW OF C550 INADVERTENTLY STARTED TKOF ROLL ON RWY 33 AT SYR WHEN CLRED ON RWY 28.

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THIS WAS A REPOSITION LEG WITH ONLY MYSELF AND THE COPLT ABOARD. WE WERE TAXIING FOR TKOF AS SHOWN IN THE DIAGRAM BELOW (FROM GA RAMP). THE TAXI INSTRUCTIONS GIVEN TO US BY GND CTL WERE 'TAXI TO RWY 25.' ALTHOUGH I AM THE CAPT AND WAS SITTING IN THE L SEAT; I WAS NOT THE PF ON THIS LEG; AND WAS ACTING AS THE COPLT. DURING THE TAXI; I HAD MY HEAD DOWN MOST OF THE TIME. I WAS PROGRAMMING OUR RTE; READING CHKLISTS; ARRANGING THE COCKPIT; NOTING THE TIMES; AND POSITIONING THE CHAIRS. AS WE CAME TO A STOP; HOLDING SHORT OF THE RWY; WE DID A BEFORE TKOF BRIEFING AND CALLED THE TWR FOR THE TKOF CLRNC. TWR RESPONDED 'CLRED FOR TKOF RWY 28;' TO WHICH WE REPLIED 'ROGER; CLRED TO GO ON TXWY 28.' AS MY COPLT BEGAN TAXIING ONTO THE RWY; I WAS SETTING BOTH OUR HDG BUGS TO 280 DEGS (FOR MY HDG). WE COMPLETED THE BEFORE TKOF CHKLIST; AND AS HE STARTED BRINGING THE PWR UP; I MADE A FINAL GLANCE ACROSS THE FLT INSTS; AND NOTICED THAT OUR HDG WAS 330 DEGS; NOT 280 DEGS. WE WERE ON RWY 33; NOT RWY 28! I IMMEDIATELY ABORTED THE TKOF AND INSTRUCTED MY COPLT TO GET THE AIRPLANE OFF RWY 33 AND ONTO RWY 28; AND BACK TAXI INTO POS ON RWY 28. I ALSO IMMEDIATELY CONTACTED THE TWR AND ADVISED THEM THAT WE HAD TAKEN A WRONG TURN AND WOULD LIKE APPROVAL TO BACK TAXI ON RWY 28. TWR RESPONDED 'THAT IS APPROVED; BUT THE NEXT TIME YOU PLAN ON TAXIING ON RWY 33; LET ME KNOW!' IT WAS OBVIOUS HE WAS AWARE OF OUR MISTAKE. SOME CONTRIBUTING FACTORS WERE MY COPLT'S NEGLECT TO PROPERLY FOLLOW THE TAXI INSTRUCTIONS; MY NEGLECT TO REALIZE HE HADN'T; AND MOST IMPORTANTLY; BOTH OUR NEGLECT TO FOLLOW SOP'S. WE COULD CLRLY HAVE REVIEWED THE TAXI DIAGRAM BEFORE TAXIING; COMPLETED SOME OF THE PRE-DEP TASKS ON THE RAMP (PRIOR TO TAXI); AND BRIEFED EACH OTHER ON WHAT TO EXPECT BEFORE IT HAPPENS. INSTEAD; OUR ACTIONS LED US TO A SIT WITH A LOT OF DISTRS AND SOME CONFUSION WHICH; IN TURN; CAUSED US TO MAKE A STUPID MISTAKE THAT COULD EASILY HAVE BEEN AVOIDED. IT IS MY RESPONSIBILITY; AS THE CAPT; TO INSURE THE FLT IS CONDUCTED IN A SAFE MANNER; AND WITHIN OUR COMPANY SOP'S. BY FOCUSING MORE ON THIS IN THE FUTURE; I'M SURE MISTAKES LIKE THIS ARE MUCH LESS LIKELY TO OCCUR.